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EURIAS Junior Fellow (1 September 2012 – 30 June 2013)
Interactions between music and mathematics are multifaceted and can be traced back into the ancient history of both disciplines. This project aims at contributing to a particular area of mathematical music theory. Recently, I proposed and explored a special formal concept called "generated tone system" (GTS). Examples of GTS's emerge in multiple musical contexts ranging from ancient music theories through Renaissance science of tuning to modern cognitive music psychology. As GTS's are found in so many different and independent streams of musical scholarship, the concept seems to capture crucial structural and cognitive characteristics of music. The main objective of the proposed project is to expand existing work and to synthesize results into a monograph on generated tone systems. The project will consist of two main parts: historical survey of the concept, and mathematical theory describing its formal properties.
Marek Žabka, Štúdie z matematickej hudobnej teórie [Studies in Mathematical Music Theory], Stimul, Comenius University, Bratislava, 2009, 239p.
Marek Žabka, "Well-Formedness in Two Dimensions: A Generalization of Carey and Clampitt's Theorem," Journal of Mathematics and Music 4 (2010), no. 1, pp. 1-30.
Marek Žabka, "Introduction to Scale Theory over Words in Two Dimensions", in Agon, C., Amiot, E., Andreatta, M., Assayag, G., Bresson, J. and Mandereau, J., eds., Mathematics and Computation in Music, Springer, Berlin, 2011
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